Items related to Nonstandard Analysis (Dover Books on Mathematics)
Synopsis
This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best." — J.-M. Lévy-Leblond, European Journal of Physics
Brief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem.
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From the Publisher
Infinitesimals have been hotly debated since the invention of calculus 300 years ago. This accessible treatment of nonstandard analysis (NSA) presents an elementary, yet rigorous account of the theory of infinitesimals and derives some known mathematical results in a nonclassical way. Provides recent solutions to mathematical questions which remained unsolved until the advent of NSA. Treatment is self-contained and includes exercises with detailed solutions. ``This wonderful little book...is simple and brilliant, deep and witty, short and far-ranging...''(--J.-M. Ley-Leblond, European Journal of Physics)
About the Author
Alain M. Robert is an active Professor of Mathematics at the University of Neuchatel in Switzerland.
"About this title" may belong to another edition of this title.
- PublisherDover Publications
- Publication date2011
- ISBN 10 0486432793
- ISBN 13 9780486432793
- BindingPaperback
- LanguageEnglish
- Number of pages176
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Paperback. Condition: new. Paperback. This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best." - J.-M. Levy-Leblond, European Journal of Physics Brief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem. This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. 1988 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780486432793
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